Mathematics Grade-9 Aptitude Assessment Tests Sanjiva Dayal IITJEE IIT JEE Foundation

138 Pages·2019·0.64 MB·English

by  Sanjiva Dayal IITJEE IIT JEE Foundation

Mathematics Grade-9 Aptitude
Assessment Tests
This book contains nine Aptitude Assessment Tests and is useful for
students and learners who are preparing for Standardized Tests,
Achievement Tests, Aptitude Tests and other competitive examinations
all over the world
Er. Sanjiva Dayal,
B.Tech. (I.I.T. Kanpur)
First Edition 2015
Sanjiva Dayal Classes For Mathematics
Head Office: A-602, Twin Towers, Lakhanpur, Kanpur-208024, INDIA.
Phone: [phone].
Mobile: [phone].
Email: [email protected].
Website: www.amazon.com/author/sanjivadayal.
ISBN-13: 978-1511696920 ISBN-10: 1511696923
Copyright © Sanjiva Dayal, Author
All rights reserved. No part of this publication may be reproduced,
distributed or transmitted in any form or by any means electronic,
mechanical, photocopying and recording or otherwise, or stored in a
database or retrieval system, including, but not limited to, in any
network or other electronic storage or transmission, or broadcast for
distance learning without the prior written permission of the Author.
i
ABOUT THE AUTHOR
Indian Institute of Technology Joint Entrance Examination (IIT-JEE) is
considered to be one of the toughest competitive entrance examinations in the
world with success ratio well below 1%. The author of this book Sanjiva
Dayal was selected in IIT-JEE in his first attempt. After completing B.Tech.
from IIT Kanpur, since the last more than 25 years, he has been teaching IIT-
JEE Mathematics to the students aspiring for success in IIT-JEE and other
engineering entrance examinations with an objective to provide training of
the highest order by way of specialized and personalized oral coaching,
teaching, training, guidance, educational facilities including tutorials, tests,
assignments, reading materials etc. and all such facilities which are helpful to
the students seeking admission in the IIT and other Engineering Institutes of
India.
His excellent teaching and result-oriented methods have combined to produce
outstanding performance by his students in the past years. A large number of
his students were selected in their First Attempt with top ranks. Most of his
students have secured admission in the IIT and other Engineering Institutes of
India and they are doing well in their engineering education and professional
career also.
Conceptual understanding of Mathematics provided by him not only helps his
students to do well in the IIT-JEE and other engineering entrance
examinations but also helps them to do well in their engineering studies
where they are pitted against the best students of the country and competition
is much more intense.
ii
ACKNOWLEDGEMENTS
I thank the Almighty God for my very existence and for providing me the
opportunity and resources to write this book.
Mother is the first teacher and father is the second teacher. My respects and
deepest gratitude to my mother Late Pushpa Dayal, my father Late Chandra
Mauleshwar Dayal, my grandfather Late Lakshmeshwar Dayal, my
grandmother Late Sarju Dayal, my maternal grandfather Late Ranbir Jang
Bahadur and my maternal grandmother Late Chandra Kishori Bahadur who
are no longer in this world but their blessings are always with me.
I am extremely thankful to all my school teachers and all my IIT Kanpur
Professors who have taught and trained me.
I am also extremely thankful to all my batch mates in IIT Kanpur because
studying and training with such brilliant persons was an amazing experience
for me which will be cherished by me throughout my life.
I am also extremely thankful to all my students because teaching and
interacting with such brilliant minds has been an amazing learning experience
for me which will be cherished by me throughout my life.
I am also extremely thankful to my wife Dr. Vidya Dayal, my sister Ms.
Smita Prakash and my niece Ms. Somya Prakash for their love, cooperation
and moral support.
I am also extremely thankful to my childhood friends Mr. Navneet Butan,
Mr. Pankaj Agarwal, Mr. Akhil Srivastava and Mr. Subir Nigam for their
love, cooperation and moral support.
I am also thankful to all other persons who have ever helped me directly or
indirectly.
I am also thankful to my student Mr. Ashutosh Verma for his help and efforts
in publishing this book.
Place: Kanpur, India.
Date: 12thApril, 2015. Sanjiva Dayal iii
PREFACE TO THE FIRST EDITION 2015
"If there is a God, he's a great mathematician."~Paul Dirac "How is an
error possible in mathematics?"~Henri Poincare "Go down deep enough
into anything and you will find mathematics."~Dean Schlicter
This book contains nine Aptitude Assessment Tests and is useful for students
and learners who are preparing for Standardized Tests, Achievement Tests,
Aptitude Tests and other competitive examinations all over the world.
All readers and students are requested and welcome to send their feedback,
comments, corrections, suggestions, improvements, mathematical theory and
questions on my email ID [email protected]. This will help in
continuous improvement and updation of this book. All readers and students
are invited to join me as friends on Facebook at URL
www.facebook.com/sanjiva.dayal and they are also invited to join my
Facebook Group "Mathematics By Sanjiva Dayal".
Place: Kanpur, India.
Date: 12th April, 2015. Sanjiva Dayal iv
CONTENTS
About The Author i
Acknowledgements ii
Preface iii
Test Paper No. 1 1.1
Test Paper No. 2 2.1
Test Paper No. 3 3.1
Test Paper No. 4 4.1
Test Paper No. 5 5.1
Test Paper No. 6 6.1
Test Paper No. 7 7.1
Test Paper No. 8 8.1 Test Paper No. 9 9.1
GRADE 9 ASSESSMENT OF MATHEMATICS
Multiple-Choice Questions: Question no. 1.1 to 1.12
Short-Answer Questions: Question no. 2.1 to 2.5
Tasks: Question no. 3.1 to 3.3
Test Paper No. 1
PREPARED BY:
Sanjiva Dayal ([email protected])
Multiple-Choice Questions
1.1
A car is moving on a circular path with a
constant speed. The distance of the car from
the center of the circular path is d. Which of
the following graph shows the relationship
between d versus time?
Circular path
Car
Center of the circular path
(a)
time (b)
time
(c)
time (d)
time
The line joining the points
x, x 2 and 2x 1,x 1 has slope equal to 1. What is the equation of this line?
(a) y x 3 (b) y x 4 (c) y 2x 1 (d) y x 2
1.3
Which of the following pair of lines are the diagonals of a rhombus?
(a) 2x 3y 5 0 and 2x 3y 5 0
(b) 3x 4y 5 0 and 4x 3y 7 0
(c) 3x 4y 5 0 and 3x 4y 2 0
(d) 2x 3y 1 0 and 4x 6y 1 0
1.4
Find the ratio of the perimeter of the square to the circumference of the circle.
(Use 22 )
7
(a) 1:1 (b) 2:1 (c) 11:7 (d) 14:11
1.5
Population of the world is about 6 billion. Population of U.S.A. is about
281,000,000. What percentage of world’s population lives in U.S.A.? (1
billion = 109 )
(a)
28.1 108
100%
6 109
7
(b) 2.81 10 100%
6 109
2
.
81
10
8
(c) 100%
6 109
9
(d) 6 10 100%
281 108
A box contains cookies. w is the weight of the box along with n cookies in it.
w, in kg, is given by the formula
w = 1.5 + 0.3n.
Weight of how many cookies is equal to the weight of the empty box?
(a) 4
(b) 5
(c) 6
(d) 7
1.7
Peter is x years old. Peter’s brother is 2 years older than Peter. Peter’s sister is
3 years younger than Peter. Age of Peter’s father is equal to the product of
the ages of his three children. What is the age of Peter’s father?
(a) x3 x2 6x (b) x3 x2 6x (c) x3 x2 6x (d) x3 x2 6x
1.8
The coordinates of the two opposite corners of a rhombus are (2,3)
(2,3) and
(5,7). What is the equation of the diagonal that is not passing
through these corners?
(a) 3x 4y 30 0
(b) 6x 8y 61 0
(c) 2x 3y 15 0 (5,7)(d) 2x 3y 15 0
1.9
Triangle ABC is a right-angled triangle. What is the length of the median AD?
A
4
(a) 5 units
(b) 6 units
(c) 7.5 units What is the perimeter of the shaded square?
B D C (d) 13 units 6
(a) 6 units 3
(b) 7 units
(c) 7.5 units
(d) 8.5 units
5
1.11
Which of the following pair of lines have the same x-intercept?
(a) 2x 3y 5 0 and 5y 4x 10 0 (b) 2x 3y 3 0 and 4x y 6 0 (c) x y 1 0 and x 3y 1 0
(d) 4x 3y 3 0 and 4x y 3 0
1.12
The sum of the interior angles of a polygon is 1080 . How many sides this
polygon has?
(a) 5
(b) 6
(c) 7
(d) 8
Short-Answer Questions
2.1
John is standing between two walls, wall A and wall B. His distance from
wall A is 6 m and from wall B is 5 m.
Wall A Wall B John
6 m 5 m
John moved towards wall B such that his distance from wall A increased by
8%. What is the percentage decrease in his distance from wall B?
Show your work
Answer: _____%
Equation of a line is
Ax By C 0
and A:B:C = 1:2:4. Find the slope, x-intercept and y- intercept of this line.
Draw this line on the coordinate plane given below.
y
10
9
8
7
6
5
4
3
2
1 x
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10